Simplify the following expression: $\dfrac{56t^3}{42t^2}$ You can assume $t \neq 0$.
$ \dfrac{56t^3}{42t^2} = \dfrac{56}{42} \cdot \dfrac{t^3}{t^2} $ To simplify $\frac{56}{42}$ , find the greatest common factor (GCD) of $56$ and $42$ $56 = 2 \cdot 2 \cdot 2 \cdot 7$ $42 = 2 \cdot 3 \cdot 7$ $ \mbox{GCD}(56, 42) = 2 \cdot 7 = 14 $ $ \dfrac{56}{42} \cdot \dfrac{t^3}{t^2} = \dfrac{14 \cdot 4}{14 \cdot 3} \cdot \dfrac{t^3}{t^2} $ $\phantom{ \dfrac{56}{42} \cdot \dfrac{3}{2}} = \dfrac{4}{3} \cdot \dfrac{t^3}{t^2} $ $ \dfrac{t^3}{t^2} = \dfrac{t \cdot t \cdot t}{t \cdot t} = t $ $ \dfrac{4}{3} \cdot t = \dfrac{4t}{3} $